smc

Note that the slope of $PQ$ is $\frac{a-b}{b-a}=-1$ and the slope of $PS$ is $\frac{b+a}{a+b}=1$. Hence, $PQ\perp PS$ and we can similarly prove that the other angles are right angles. This means that $PQRS$ is a rectangle. By distance formula we have $(a-b{)}^2+(b-a{)}^2\ast 2\ast (a+b{)}^2=256$. Simplifying we get $(a-b)(a+b)=8$. Thus $a+b$ and $a-b$ have to be a factor of 8. The only way for them to be factors of $8$ and remain integers is if $a+b=4$ and $a-b=2$. So the answer is $\boxed{4}$